Fixed Point Theorems With Application To Generalized Equilibrium Problems And Splitting Inertial Proximal Algorithm Of Mixed Variational Inequalities

This paper is concerned with fixed point theorems and their applications and algorithm of variational inequalities. In chapter one, acyclic mappings is discussed. Some new fixed point theorems for a family of set-valued mappings in product space of topological vector spaces are obtained. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems are established. Chapter two, some new collectively fixed point theorems and existence theorems of maximal element involving better admissible mappings in G ?convex spaces are proved. As applications some equilibrium existence theorems of abstract economies are obtained. In chapter three, a class of mixed variational inequalities is studied. By using the ε?enlargements of maximal monotone operators, we get a splitting inertial proximal algorithm. Moreover, we also prove the weak convergence criteria.